Quantum mechanics and field theory with momentum defined on an anti-de-Sitter space

Relativistic dynamics with energy and momentum resricted to an anti-de-Sitter space is presented, specifically in the introduction of coordiate operators conjugate to such momenta. Definition of functions of these operators, their differentiation and integration, all necessary for the development of dynamics is presented. The resulting algebra differs from the standard Heisenberg one, notably in that the space-time coordinates do not commute among each other. The resulting time variable is discrete and the limit to continuous time presents difficulties. A parallel approach, in which an overlap function, between position and momentum states, is obtained from solutions of wave equations on this curved space are also investigated. This approach, likewise, has problems in the that high energy behavior of these overlap functions precludes a space-time definition of action functionals.Comment: 10 pages, presented at a Conference in Honor of Murray Gell-Mann's 80th Birthday, 24-26 February, 2010, Nanyang Technical University, Sigapor

Breaking of de Sitter Symmetry

We show that an interacting spin-0 field on a de Sitter space background will break the underlying de Sitter symmetry. This is done first for a (1+1) de Sitter space where a boson-fermion correspondence permits us to solve certain interacting theories by transforming them into free ones of opposite statistics. A massless boson interacting by a sine-Gordon potential is shown to be equivalent to a free massive fermion with the mass depending on the de Sitter time thus breaking the symmetry explicitly. We then show that for larger dimensions and any boson potential, to one loop, an anomaly develops and the currents generating the de Sitter transformations are not conserved.Comment: Talk at Quarks, Strings and the Cosmos - H\'{e}ctor Rubinstein Memorial Symposium, August 09-11, 2010 AlbaNova)Stockholm) Sweden 12 pages, 1 figur

Equations of Motion for Spinning Particles in External\\Electromagnetic and Gravitational Fields

The equations of motion for the position and spin of a classical particle coupled to an external electromagnetic and gravitational potential are derived from an action principle. The constraints insuring a correct number of independent spin components are automatically satisfied. In general the spin is not Fermi-Walker transported nor does the position follow a geodesic, although the deviations are small for most situations.Comment: 7 pages set in Revtex I

Screening of Very Intense Magnetic Fields by Chiral Symmetry Breaking

In very intense magnetic fields, $B > 1.5\times 10^{14}$ T, the breaking of the strong interaction $SU(2)\times SU(2)$ symmetry arranges itself so that instead of the neutral $\sigma$ field acquiring a vacuum expectation value it is the charged $\pi$ field that does and the magnetic field is screened. Details are presented for a magnetic field generated by a current in a wire; we show that the magnetic field is screened out to a distance $\rho_o\sim I/f_\pi m_\pi$ from the wire.Comment: 7 pages (using macropackage REVTEX II